Measuring forecast performance in the presence of observation error

A new framework is introduced for measuring the performance of probability forecasts when the true value of the predictand is observed with error. In these circumstances, proper scoring rules favour good forecasts of observations rather than of truth and yield scores that vary with the quality of the observations. Proper scoring rules thus can favour forecasters who issue worse forecasts of the truth and can mask real changes in forecast performance if observation quality varies over time. Existing approaches to accounting for observation error provide unsatisfactory solutions to these two problems. A new class of ‘error‐corrected’ proper scoring rules is defined that solves both problems by producing unbiased estimates of the scores that would be obtained if the forecasts could be verified against the truth. A general method for constructing error‐corrected proper scoring rules is given for the case of categorical predictands, and error‐corrected versions of the Dawid–Sebastiani scoring rule are proposed for numerical predictands. The benefits of accounting for observation error in ensemble post‐processing and in forecast verification are illustrated in three data examples that include forecasts for the occurrence of tornadoes and of aircraft icing.